The Cosmic-Ray Positron Excess from a Local Dark Matter Over-Density

The cosmic-ray positron excess from a local Dark Matter over-density

Andi Hektor,1, 2 Martti Raidal,1, 3 Alessandro Strumia,1, 4 and Elmo Tempel1, 5 1National Institute of Chemical Physics and Biophysics, Ravala 10, 10143 Tallinn, Estonia 2Helsinki Institute of Physics, P.O. Box 64, FI-00014, Helsinki, Finland 3Institute of Physics, University of Tartu, Estonia 4Dipartimento di Fisica dell’Universitàdi Pisa and INFN, Italia 5Tartu Observatory, Observatooriumi 1, 61602 Toravere, Estonia (Dated: September 15, 2021) We show that the cosmic-ray positron excess measured by PAMELA and AMS could be induced by Dark Matter annihilations in a local over-density. In such a context leptophilic DM is not needed and good fits to positron data, in agreement with antiproton and gamma-ray measurements, are obtained for DM annihilations to WW , hh, ZZ, tt¯, b¯b, qq¯ channels. The classic Dark Matter candidates, such as the pure supersymmetric Wino with standard thermal annihilation cross-section, can fit the positron excess, without invoking any additional assumption on Dark Matter properties.

Introduction. The new AMS02 measurement [1, In this paper we propose a solution to the positron 2] of the cosmic ray positron energy spectrum up anomaly that does not require additional ad hoc assump- to 350 GeV confirms with better precision the ear- tions on DM properties. The idea is that the positron lier claim by PAMELA [3] and FERMI [4] of a rising anomaly is a local effect arising from DM annihilations positron/electron fraction. Such a spectral feature de- in a local DM over-density. DM density fluctuations, that mands either non-conventional models of the astrophysi- are not gravitationally bound, are predicted to occur and cal background [5] or new sources, such as pulsars [6–11] disappear continuously everywhere in our Galaxy by the or annihilations of weakly interacting Dark Matter (DM). cold DM paradigm. The measured positron excess could then originate from such a local over-density even with DM can explain the positron excess compatibly with the standard thermal annihilation cross-section.1 the absence of a similar excess in the antiproton flux This implies observable energy spectra of e±, p,¯ γ dif- provided that the DM of the main Milky Way halo an- ferent from the standard case where DM annihilates in nihilates predominantly into the Standard Model (SM) all the Galaxy. Our most important result is that DM leptons with a cross-section 2 − 3 orders of magnitude annihilations into the usual theoretically favoured chan- larger than the annihilation cross-section predicted by nels, the hypothesis that DM is a thermal relic [12–14]. Such a large cross-section today may result from a Sommer- W W, ZZ, hh, qq,¯ b¯b, tt,¯ . . . , feld enhancement [12], maybe mediated by new hypo- thetical GeV scale vectors [13]. However, this scenario is can now reproduce the energy spectrum of the positron severely constrained by the absence of associated gamma- excess, while purely leptonic channels become dis- rays from the galactic center, from dwarf galaxies and in favoured. This is because positron energy losses can now the diffuse background [15–20]. Additional constraints be neglected, such that a more shallow energy spectrum arise from observations of the cosmic microwave back- at production is needed to fit the positron excess. This re- ground (CMB) [18, 21–23]. Such constraints challenge sult implies that the conventional WIMP DM models are various aspects of current DM theories — DM origin as preferred by data without invoking additional assump- a thermal relic, early cosmology, simulations of the Milky tions. We will show that constraints fromp ¯ and γ are arXiv:1307.2561v2 [hep-ph] 12 Jul 2013 Way DM halo density profile, as well as particle physics satisfied. models of the DM. Additional information that may discriminate between DM models is provided by DM direct detection experi- Furthermore, even DM annihilations into leptons are ments. If the local DM over-density exists today around challenged, because the final state e± loose almost all us, the DM coupling to nuclei must be suppressed. This of their energy through inverse Compton scattering on favours, for example, pure Wino DM or Minimal Dark galactic star-light and CMB, producing a secondary flux Matter scenarios, where DM couples to matter only via of energetic photons. Such Inverse Compton photons can be compatible with gamma-ray observations provided that DM in the Milky Way has a cored (such as an isothermal) density profile [24–31]. 1 Various past articles considered the possibility of interpreting the The non-observation of such Inverse Compton photons positron excess in terms of enhanced DM matter annihilations from a variety of different kinds of nearby DM sub-structures, favors the possibility that the positron excess is local, such as clumped sub-haloes [32], black holes [34], dark stars [33], rather than present in all the Milky Way. a dark disk [35]. 2 a W -boson loop. If, instead, the DM over-density has 0.50 Bpart =1 already disappeared, and today we observe a remnant R=0.5 kpc Diffusion: MIN position excess trapped by the Galactic magnetic fields, 0.20 é é é í é typical WIMP DM model are viable candidates. é é í é é é 0.10 éééééé éé L í ééé - í é e ééééé

F é é é ééééé í + éíé íé ééíéé + éíé é í í íééé é The local DM over-density. N-body simulations e 0.05 íé é ééíéééééé F H + e of cold DM structure formation predict a wide spectrum F

í PAMELA of density and velocity fluctuations in any DM halo such 0.02 é AMS02 as our Galaxy [36]. Only a very small fraction of the den- ΧΧ®bb 1893 GeV, 45Ρ ΧΧ® Ρ 0.01 WW 1194 GeV, 41 sity fluctuations develop high enough over-density, a few ΧΧ®hh 2124 GeV, 50Ρ H L Background hundred times over the local average, to become gravi- H L tationally bound sub-halos. A fluctuation with density ρ 10 H 50L 100 500 1000 5000 Energy GeV and radius R is gravitationally bound provided that the escape velocity from it is smaller than the typical local FIG. 1: Best fits of the positronH fractionL from DM annihila- DM velocity dispersion, tions to WW , hh, ¯bb for parameters indicated in the figure. Over-densities are indicated as ρloc and given relative to the r 8π average density ρ0. v = G R2ρ 10−3, (1) esc 3 N i.e. for ρ/ρ 200×(kpc/R)2, where ρ = 0.4 GeV/cm3 0 0 To compute the diffusion effects we assume the is the average DM density around the Sun. Those dense MIN/MED/MAX diffusion models of [39], as described fluctuations collapse gravitationally and develop cuspy in [38]. The number densities f(~x,t, E) of e+ and their NFW or Einasto like profile similarly to the main halo. fluxes Φ + = cf/4π are well approximated by neglecting However, the vast majority of fluctuations just occur e the energy loss term in the time-independent diffusion and disappear continuously without affecting large scale equation, that becomes simply structure formation. Those over-density regions have 2 shallow profiles, such as Gaussians, since they are not dNe+ 1 ρ dNe+ − K(E)∇2f = Q = hσvi , (2) gravitationally bound. dE 2 M 2 dE In this work we assume that there exists, or there ex- where K(E) is approximatively given by the Larmor isted not long time ago, a local DM over-density with radius in the local turbulent Milky Way magnetic a radius of few hundred pc. Such an assumption is in field. Analyses of cosmic ray data suggest K(E) = δ agreement with the determination of local DM density K0(E/GeV) with δ = 0.85 − 0.46 and K0 = (0.016 − at the distance of Sun. The latter is measured by the 0.0765) kpc2/Myr [39]. movement of stars in a cylinder of radius 1 kpc extend- Assuming, for simplicity, that we live at the center ing ±4 kpc in both directions around the Galactic disc. of a spherical excess with constant local density ρ and A local over-density with radius R = 100 pc forms just radius R, and neglecting DM annihilations outside it, 1/6000 of this volume, not affecting the average result. the solution is In fact, several over- and under-density fluctuations are 3Γ dNe+ expected to occur in such a big volume. Furthermore, a Φ + = , (3) e 32π2K(E)R dE moderate local over-density is compatible with solar sys- tem gravitational measurements that imply a local DM where Γ is the total DM annihilation rate in the local density smaller than ρ/ρ0 < 15000 [37]. over-density: Z 4πR3 1 ρ2 Γ = dV Q = hσvi . (4) Explaining the positron excess. We now try to 3 2 M 2 interpret the measured positron excess as due to DM annihilations in a local DM over-density. As a result, we The shape and location of the local excess only affect the obtain the size and density of such a fluctuation from overall numerical factor in eq. (3), leaving unaffected the the AMS and PAMELA data. This will allow us to later main feature: the positron energy spectrum at detection predict the associated gamma-ray and antiproton fluxes. is given by the positron energy spectrum at production In our exploration we follow the model independent ap- over the diffusion factor K(E). proach introduced in [12, 38]. We allow DM to annihilate The boost factor B that enhances the positron DM flux into all possible two-body SM final states with the stan- with respect to the standard scenario can be expressed dard thermal relic cross-section hσvi ≈ 3 · 10−26 cm2. as The energy spectra of the various stable SM particles + (e , p,¯ γ, ν, . . .) are computed with PYTHIA8. B = Bpart × Blocal, (5) 3

300 10 ΤΤ 337 GeV, 18Ρ gg bb 2124 GeV, 30Ρ 250 tt 2383 GeV, 36Ρ H L gg 2674 GeV, 66Ρ 3 H L e qq

WW 1504 GeV, 37Ρ F H L

200 p ZZ 1504 GeV, 31Ρ

H L F hh 2124 GeV, 33Ρ bb

2 H L

Χ 1 tt H L 150 ratio hh H L ZZ Flux 100 0.3 WW

Bpart =1 R=0.5 kpc 50 0.1 0.01 0.03 0.1 0.3 1 500 1000 2000 5000 1´104 2´104 DM mass in GeV EM

2 FIG. 2: Fit to the positron fraction: χ as function of the DM FIG. 3: Predicted Φp¯/Φe+ for various SM annihilation chan- + − mass for diﬀerent DM annihilation channels. nels into W W , ZZ, hh, tt,¯ b¯b, qq,¯ gg for M ∼ 1 TeV.

where B ∝ ρ2 is the boost induced by the local DM local tion channels are different. Measurements of the positron over-density that we are considering, and B is a pos- part fraction at higher energy will provide more informations sible extra boost due to particle physics, not needed in on the properties of DM. our context, but that could be anyhow present. For example, DM with SM weak interactions and heavier than Notice also that the required DM over-densities for the best fit channels are of order 40 − 50: smaller than the MDM > MW /α2 ≈ few TeV has an annihilation cross section enhanced at low velocity by the electroweak SM over-density that would form gravitationally bound sub- haloes. In presence of particle boost factor Bpart of order Sommerfeld effect, thereby producing Bpart > 1. 10, the needed over-density would be reduced down to In Fig. 1 we plot the best fit spectra of the positron ρ ∼ 5ρ0. ¯ fraction from the DM annihilations to WW , hh and bb Based on this scenario, one expects a directional asym- channels as functions of positron energy. We assumed metry of the positron signal, at the level or smaller than a spherical local over-density with radius R = 500 pc. the asymmetry produced by nearby pulsars or DM sub- 2 The χ of the fits for the various annihilation channels haloes [10], and thereby compatible with existing data. as function of the DM mass are presented in Fig. 2. The Given that we do not know the location of the local DM required over-densities are also presented in the figures. excess relative to us, such asymmetry cannot be precisely The main result from Figs. 1, 2 is that only DM an- predicted. nihilations to channels like WW , ZZ, gg, hh, ¯bb, tt¯ give Furthermore, the positron excess should also be visi- good fits to data while leptonic channels give very poor ble as a small bump in the e+ + e− cosmic ray energy (e+e−, µ+µ−) or poor (τ +τ −) fits. spectrum. The experimental situation is at the moment The reason for this result is that in our scenario the unclear: the recent measurement from AMS [2] contra- positron anomaly is a local phenomenon so that positron dicts earlier measurements from ATIC and FERMI, that energy losses can be neglected. Therefore, the measured contained two different hints of bumps. Thereby we can- rise of the positron fraction is reproduced by injecting not derive any safe conclusion from present data. a shallow initial positron spectrum dNe+ /dE into the Galactic environment. This is exactly opposite to the scenario in which the positron excess arises from DM annihilations in the main Galactic halo thanks to a large Implications for antiprotons. Fixing the local DM over-density and the DM parameters as in Figs. 1, particle physics boost factor Bpart 1. In the latter case the positron energy loss effects are significant and the in- 2, we are able to predict the antiproton fluxes from the jected spectrum must be hard to fit data [24]. This is the local over-density due to DM annihilations. reason why only leptonic channels are able to provide In the relevant energy rangep ¯ and e+ diffuse in the good fits in that case [24]. Therefore, particle physics same way, because they have the same electric charge models that are able to fit the data are completely dif- (up to the sign), because they are both ultra-relativistic, ferent in the two cases. and because we can neglect positron energy losses and AMS data prefer DM with masses 1 − 5 TeV. As seen p¯ interactions. Thep ¯ flux is then given by eq. (3), just in Fig. 1, the high energy behaviour of different annihila- inserting the appropriate prompt energy spectrum. The 4

spherical constant over-density with radius R. The ratio í í Bpart =1 í í í í í í í í í í í R=0.5 kpc between photons and positrons is predicted as - í 10 5 í í Diff . model: MIN í í í í Φγ 2K dNγ /dE L

1 -6 - 10 í = . (8) sr

1 í PAMELA Φ + R dN + /dE

- í e e s

2 ΧΧ ®hh 2124 GeV, 50Ρ - -7 ΧΧ ® Ρ cm 10 bb 1893 GeV, 45 ΧΧ ® Ρ Up to the geometry-dependent order one factor, the as- WW 1194 GeV, 41

GeV H L H Background

ap H L trophysical factor K/R can be intuitively understood as F -8 2 10 E H L follows. For all particles, ﬂuxes are inversionally pro-

10-9 portional to their speed. Photons travel at the speed of + light, while e diffuse in a time T for√ a distance R with 10-10 an average velocity given by R/T ' KT /T ' K/R. 1 10 100 1000 Energy GeV The ratio Φγ /Φe+ depends on the uncertain diffusion parameter K(E) and on the size of the bubble. Fig. 5 H L FIG. 4: Predicted p¯ fluxes from the local DM over-density shows the predicted DM γ flux for a bubble with R ≈ (long dashed) and from the main halo (short dashed) for the + 0.5 kpc and for the MIN propagation model. The γ flux parameters that in Fig. 1 provide the best fits to the e excess. from local DM annihilations is a factor of few below the We also show the estimated astrophysical p¯ background. two measured γ fluxes plotted in Fig. 5: 1. The pink band is the diffuse isotropic γ-ray background, as extracted from the FERMI collabora- prediction is: tion [42]. Φ dN /dE p¯ = p¯ . (6) 2. The slightly higher gray band is extracted by us Φe+ dNe+ /dE from FERMI data, following a simpler procedure. We subtracted known point-like sources and re- All non-leptonic SM annihilation channels predict that duced the Galactic gamma-ray background by re- this ratio is ≈ 0.5 at the relevant value of E/M ≈ 0.1, stricting the observation region to high Galactic see Fig. 3. latitudes, |b| > 60◦. This implies a predictedp ¯ DM flux at the level of the flux observed by PAMELA, as presented in Fig. 4. We do not show the expected astrophysical γ-ray back- The grey area in Fig. 4 is the antiproton astrophys- ground because we do not know any reliable estimate of ical background, as estimated in [40]. Given that the it. astrophysicalp ¯ background is believed to have a ∼ 30% We here neglected the Inverse Compton γ ray flux, uncertainty [41], there is some tension with the PAMELA because it is strongly reduced with respect to the stan- data at higher energy. The issue will be soon clarified by dard scenario, where it is problematic, by our assump- improved AMS measurements of thep ¯ flux. tions that the e+ excess is just local. Finally, we point out that, while the main features of For comparison, the standard scenario without a local our results have been explained with simple approxima- tions, our numerical results have been derived from a full DM over-density predicts a Φp¯/Φe+ which is uncertain and higher than in eq. (6), because energy losses from dis- numerical study where we have taken into account en- ± tant DM annihilations around the center of the Galaxy ergy losses for e and other small effects. In Figs. 4 and 5 we also plotted the contributions to the gamma-ray reduce Φe+ but not Φp¯, and because the amount of Φp¯ that reaches us depends on the unknown volume of the and antiproton fluxes coming from regions of the Milky Galactic diffusion region. This is why, in the standard Way outside from the dominant local over-density. We scenario,p ¯ bounds are stronger and one needs to select see that such contribution is so small that the analy- leptophilic DM particle physics models that avoid anni- sis would remain unchanged in presence of a moderate hilations intop ¯. Bpart ∼ 10, or even larger.

Implications for DM direct detection. We found Implications for gamma-rays. The γ ﬂux is pre- that the positron excess can be reproduced as due to dicted as DM annihilation with the standard thermal-relict cross Z 2 hσvi dNγ 1 ρ 3Γ dNγ section, assuming a local DM over-density with ρ ∼ Φγ = ds = , (7) 2 2 2 40ρ0/Bpart (see ﬁgures 1, 2). Here, Bpart ≥ 1 is a 4π dE l.o.s. 2 M 16π R dE boost factor of particle physics origin (e.g. Sommerfeld where in the last expression we evaluated the line-of-sight enhancement), that could be larger than one even if this integral by assuming again that we are at the center of a is not needed in our scenario. 5

10-6 density. In such a context, it is not necessary to assume Bpart =1 R=0.5 kpc leptophilic DM annihilations — on the contrary DM an- Difusion: MIN nihilations into the theoretically favoured channels WW , 10-7 ¯ ¯ L ZZ, gg, hh, bb, tt can explain the data. This scenario pre- 1 - sr 1

- dictsp ¯ and γ ﬂuxes from DM annihilations at the level s 2 - Fermi LAT, b >60° -8 cm 10 1Σ of Fermi LAT of present measurements. In particular, AMS can test Fermi LAT isotropic diffuse GeV H È È this scenario performing and improved measurement of Γ ΧΧ ®bb 1893 GeV, Ρloc=44 Ρ F 2

E ΧΧ ® Ρ = Ρ WW 1194 GeV, loc 35 thep ¯ flux. In such a context, the positron excess prefers -9 ΧΧ ®hh 2124 GeV, Ρloc=46Ρ 10 H L ‘classical’ WIMP DM candidates with suppressed cou- H L H L pling to nuclei, such as the pure Wino, without additional assumptions on DM properties nor invoking any exotic 10-10 20 50 100 200 500 1000 2000 particle physics to boost the annihilation cross-section. Energy GeV Finally, if the positron excess is not due to DM an- FIG. 5: Predicted gamma-ray fluxesH L from the local over- nihilations, our results imply a bound on the local DM density (long-dashed) and the main halo (short dashed) for the same parameters as in Fig 1. The bands show γ- density that is stronger than the direct bound [37] for measurements: (gray) γ-ray flux from the polar regions (|b| > M ∼ 1 TeV and for a radius R > 0.1 pc of the local 60◦) measured by Fermi LAT and (pink) the isotropic compo- over-density, and under the assumption of a thermal DM nent of γ-ray sky estimated by the Fermi LAT Collaboration. annihilation cross section.

Acknowledgement. AH thanks Peter H. Johansson The boost of indirect DM detection signals, propor- for very helpful discussions. This work was supported by tional to ρ2, is accompanied by a smaller boost of DM the ESF grants 8499, 8943, MTT8, MTT59, MTT60, direct detection signals, proportional to ρ. In order to ex- MJD52, MJD140, JD164, MJD298, MJD272 by the re- plain the negative DM direct searches in Xenon100 [43], current financing SF0690030s09 project and by the Euro- the DM spin-independent cross-section to nuclei must pean Union through the European Regional Development be smaller than about 10−45 cm2 for M ∼ TeV. This Fund. happens naturally in various theoretically motivated DM models. For example, if DM is a pure supersymmetric Wino (or, equivalently, a Minimal Dark Matter fermion triplet), the [1] AMS Collaboration, Phys. Rev. Lett. 110, 14 (2013). DM relic abundance fixes its mass to be 2.5 TeV. Such a [2] Talk by S. Ting at the ICRR 2013 conference and AMS02 DM candidate gives a good fit to the position excess, as web site. seen in Fig. 1. At the same time, such particle couples [3] Fermi LAT Collaboration, Phys. Rev. Lett. 108, 011103 to nuclei only via a W -boson loop, giving a small cross (2012) [arXiv:1109.0521]. section σ ∼ 0.6 10−46 cm2 [44], compatible with the [4] PAMELA Collaboration, Nature 458, 607 (2009) SI [arXiv:0810.4995]. negative results of Xenon100. [5] P. Blasi, Phys. Rev. Lett. 103 (2009) 051104 Alternatively, in many models DM couples to SM par- [arXiv:0903.2794]. P. Mertsch and S. Sarkar, Phys. Rev. ticles only via the Higgs doublet. Such models gener- Lett. 103 (2009) 081104 [arXiv:0905.3152]. ically predict DM annihilations into hh and may have [6] D. Hooper, P. Blasi and P. D. Serpico, JCAP 0901, 025 (2009) [arXiv:0810.1527]. small enough DM/nucleon cross section σSI. In particular, scenarios in which the electroweak breaking scale is [7] D. Malyshev, I. Cholis and J. Gelfand, Phys. Rev. D 80, 063005 (2009) [arXiv:0903.1310]. induced via the Higgs boson mixing with a singlet scalar [8] V. Barger, Y. Gao, W. Y. Keung, D. Marfatia from the dark sector [45–47] predict generically that σSI and G. Shaughnessy, Phys. Lett. B 678, 283 (2009) is suppressed by the small mixing angle. [arXiv:0904.2001]. [9] FERMI-LAT Collaboration, Astropart. Phys. 32, 140 If, instead, the local DM over-density fluctuation has (2009) [arXiv:0905.0636]. already disappeared today, and PAMELA, AMS measure [10] T. Linden and S. Profumo, arXiv:1304.1791. the remnant of the positron excess trapped by Galactic [11] I. Cholis and D. Hooper, arXiv:1304.1840. magnetic fields, no additional constraints on our scenario [12] M. Cirelli, M. Kadastik, M. Raidal and A. Strumia, Nucl. occurs from DM direct detection experiments. Phys. B 813, 1 (2009) [arXiv:0809.2409]. [13] N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer and N. Weiner, Phys. Rev. D 79, 015014 (2009) Conclusions. We have shown that the positron ex- [arXiv:0810.0713]. cess measured by PAMELA and confirmed by AMS could [14] I. Cholis, G. Dobler, D. P. Finkbeiner, L. Goode- be due to DM annihilations enhanced by a local DM over- nough and N. Weiner, Phys. Rev. D 80, 123518 (2009) 6

[arXiv:0811.3641]. L. Bergstrom, T. Bringmann, I. Cho- bins and K. M. Zurek, Phys. Rev. D 79 (2009) 103513 lis, D. Hooper and C. Weniger, arXiv:1306.3983. [arXiv:0812.3202]. P. Brun, T. Delahaye, J. Diemand, [15] P. Meade, M. Papucci, A. Strumia and T. Volansky, Nucl. S. Profumo and P. Salati, Phys. Rev. D 80, 035023 (2009) Phys. B 831, 178 (2010) [arXiv:0905.0480]. [arXiv:0904.0812]. M. Kuhlen and D. Malyshev, Phys. [16] M. Cirelli, P. Panci and P. D. Serpico, Nucl. Phys. B 840 Rev. D 79, 123517 (2009) [arXiv:0904.3378]. J. M. Cline, (2010) 284 [arXiv:0912.0663]. A. C. Vincent and W. Xue, Phys. Rev. D 81, 083512 [17] M. Papucci and A. Strumia, JCAP 1003 (2010) 014 (2010) [arXiv:1001.5399]. [arXiv:0912.0742]. [33] C. Ilie, K. Freese and D. Spolyar, New J. Phys. 13 (2011) [18] G. Huetsi, A. Hektor and M. Raidal, Astron. Astrophys. 053050 [arXiv:1008.0348]. 505, 999 (2009) [arXiv:0906.4550]. [34] R. Saito and S. Shirai, Phys. Lett. B 697 (2011) 95 [19] Fermi-LAT Collaboration, Phys. Rev. Lett. 107 (2011) [arXiv:1009.1947]. 241302 [arXiv:1108.3546]. [35] I. Cholis and L. Goodenough, JCAP 1009 (2010) 010 [20] Fermi-LAT Collaboration, Astrophys. J. 761, 91 (2012) [arXiv:1006.2089]. [arXiv:1205.6474]. [36] M. Kamionkowski, S. M. Koushiappas and M. Kuhlen, [21] S. Galli, F. Iocco, G. Bertone and A. Melchiorri, Phys. Phys. Rev. D 81 (2010) 043532 [arXiv:1001.3144]. Rev. D 80, 023505 (2009) [arXiv:0905.0003]. [37] N. P. Pitjev and E. V. Pitjeva, Astron. Lett. 39 (2013) [22] T. R. Slatyer, N. Padmanabhan and D. P. Finkbeiner, 141 [arXiv:1306.5534]. Phys. Rev. D 80, 043526 (2009) [arXiv:0906.1197]. [38] M. Cirelli, G. Corcella, A. Hektor, G. Hutsi, M. Kadastik, [23] M. Cirelli, F. Iocco and P. Panci, JCAP 0910, 009 (2009) P. Panci, M. Raidal and F. Sala et al., JCAP [arXiv:0907.0719]. 1103, 051 (2011) [Erratum-ibid. 1210, E01 (2012)] [24] Addendum to M. Cirelli, M. Kadastik, M. Raidal and [arXiv:1012.4515]. A. Strumia, Nucl. Phys. B 813, 1 (2009). Updates re- [39] T. Delahaye, R. Lineros, F. Donato, N. Fornengo sulting from from the analyses of new AMS-2 data are and P. Salati, Phys. Rev. D 77, 063527 (2008) available in arXiv:0809.2409. [arXiv:0712.2312]. [25] J. Kopp, arXiv:1304.1184. [40] M. Cirelli and G. Giesen, JCAP 1304 (2013) 015 [26] A. De Simone, A. Riotto and W. Xue, arXiv:1304.1336. [arXiv:1301.7079] and references therein. [27] Q. Yuan, X. -J. Bi, G. -M. Chen, Y. -Q. Guo, S. -J. Lin [41] C. Evoli et al., Phys. Rev. D 85, 123511 (2012). and X. Zhang, arXiv:1304.1482. [42] Fermi-LAT Collaboration, Phys. Rev. Lett. 104 (2010) [28] H. -B. Jin, Y. -L. Wu and Y. -F. Zhou, arXiv:1304.1997. 101101 [arXiv:1002.3603]. [29] Q. Yuan and X. -J. Bi, arXiv:1304.2687. [43] XENON100 Collaboration, Phys. Rev. Lett. 109, 181301 [30] M. Ibe, S. Iwamoto, S. Matsumoto, T. Moroi and (2012) [arXiv:1207.5988]. N. Yokozaki, arXiv:1304.1483. M. Ibe, S. Matsumoto, [44] J. Hisano, K. Ishiwata and N. Nagata, Phys. Lett. B 690, S. Shirai and T. T. Yanagida, arXiv:1305.0084. 311 (2010) [arXiv:1004.4090]. [31] Y. Kajiyama, H. Okada and T. Toma, arXiv:1304.2680. [45] M. Heikinheimo, A. Racioppi, M. Raidal, C. Spethmann A. Fowlie, K. Kowalska, L. Roszkowski, E. M. Sessolo and and K. Tuominen, arXiv:1304.7006. Y. -L. S. Tsai, arXiv:1306.1567. K. R. Dienes, J. Kumar [46] M. Heikinheimo, A. Racioppi, M. Raidal, C. Spethmann and B. Thomas, arXiv:1306.2959. and K. Tuominen, arXiv:1305.4182. [32] D. Hooper, J. E. Taylor and J. Silk, Phys. Rev. D 69 [47] T. Hambye and A. Strumia, arXiv:1306.2329. (2004) 103509 [hep-ph/0312076]. D. Hooper, A. Steb-